A Special Case of Multi-Way Relay Channel: When Beamforming is not Applicable

In this paper, we study a special case of multi-way relaying channel, to which traditional beamforming cannot achieve the best performance due to insufficient antennas. A new transmission protocol is proposed by aligning the messages from the same pair with the help of relay precoding. As a result, inter-pair interference can be avoided and intra-pair interference can be coped with by using network coding. Then analytic results, such as the ergodic sum rate and the outage probability, are developed for the proposed protocol. The numerical results are also provided to demonstrate the performance of our proposed scheme. To improve the diversity gain of the proposed scheme, an optimal scheme is also presented.